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I don't know. Probably something involving unstable elements. Lots of type specimens of minerals are only known (or described in the case of ephemeral minerals) from one sample. However, I'll defer to a chemist or physicist on this one. I haven't done any crystallography or related activites for years. Most of my work has been in sedimetary geology and biostratigraphy...basically paleontology via geology.

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I don't think we'd ever find any minerals made of unstable elements like Technetium---we'd have to make them in a lab. The problem is that any of the elements that we find on the earth was here since the beginning, i.e. four billionish years. Elements like Technetium have had enough time to go through many half-lives---any technetium that was here when the earth was formed is long gone by now.

Californium is rather expensive, from what I have heard. As are most of the synthetic elements, I guess.

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I think for the purposes of this discussion the definition of "mineral" has to include "naturally occurring." Otherwise every time somebody creates one microgram of crystal in a lab after the previous one has been tested to destruction, it becomes the new recordholder.

What's interesting is that we can often predict with good certainty that certain crystal structures should exist naturally without ever actually discovering them.

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This is the creeping overlap between physics and mathematics. Relativity, uncertainty, string theory, these are all derived more from math than physics. I have commented on this in the Cosmology threads. Some of the new explanations of how the universe works seem like they belong in a math book.

You couldn't at least have waited until somebody asked, "What is the rarest animal?" Not to mention, that is a purely subjective observation. Not everyone has experienced this "rarity" of which you speak. As I've said before, I think you could do a lot by losing the visiting Klingon anthropologist dialect. If you're looking for "a female with whom to couple" you're not very likely to find one.

It has been said a few times i believe but it probably hasnt been found yet.
Or do you mean the rarest mineral known to man ? I which case i dont know. I dont think they even keep track of which mineral is rarest.

is ice a mineral? I know it melts, but isn't lava just melted mineral?

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Not quite, both arent. A mineral is an element or chemical compound that is normally crystalline and that has been formed as a result of geological processes.
A rock is an aggregate of minerals and need not have a specific chemical composition. Lava is molten rock.

It's probably mostly a structural thing in categorization. I'm willing to bet, however, that there are at least several tens to hundreds of entirely new species each year.

The rarest extant mineral that I know of is endemic to California - benitonite (not to be confused by the ubiquitous clay, bentonite), named after San Benito county, which is the only known location. Actually, Simon & Schusters documents quite a few minerals with single-principalities.

SERENDIBITE is the rarest gem. It has an unusually complex formula consisting of calcium, magnesium, aluminum, silicon, boron and oxygen. So far there exist three faceted specimens of 0.35 carats, 0.55 carats and 0.56 carats. The first two were discovered by rare stone specialist D. P. Gunasekera. The smaller was sold for about $14500 per carat.

this all changes day to day though depending on new deposits discovered.

Astatine is the rarest chemical, opnly 75 mg in the earths crust. partly due to its tiny hlaflife and speed of decay.

Edit: I looked online and it seems Lutetium ranks as the rarest element on earth. With another source generalising with iridium.

SERENDIBITE is the rarest gem. So far there exist three faceted specimens of 0.35 carats, 0.55 carats and 0.56 carats.

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This is getting pretty philosophical here. If the rarest mineral we know of only has three specimens, how do we know there isn't something rarer that we just haven't happened to find yet?

The smaller was sold for about $14500 per carat.

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That's not very expensive. You'd think they could have gotten more for it on an e-Bay auction.

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It must not be very attractive as a gemstone, or these guys never took Marketing 101A.

Absolutely. As Enmos explained, the definition of a mineral is a crystalline structure and all gemstones have that by definition. It's what gives them the refractive property that makes them beautiful

So then is a cubic zirconia a mineral?

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I think we've reached the consensus that a mineral has to be naturally occurring. Cubic zirconia is synthetic and never occurs naturally. Contrary to casual misinformation, cubic zirconia is not a synthetic zircon--which is a mineral and a natural gemstone. Its molecules contain atoms of the element zirconium (symbol Zr) and other atoms, as do the molecules in a zircon crystal, but they do not have the same composition and structure.

Zircon is an interesting mineral, extremely sturdy. I read once that the oldest piece of matter known to be in existence is a zircon crystal.

Well the thing about crystal is that it can exist as one large object or be divided into many smaller ones. That's one of the basic mathematical properties of the crystalline structure.

As a purely aesthetic judgment, we usually think of "a crystal" as convex. If the material has concavities, we perceive them as separating "one crystal" from another, even if it's all one big object that you'd have to hit with a hammer to separate. On the other hand, in science we usually talk about "crystals" as being distinct, separated objects.

So a physicist would probably call the object in your picture one crystal, whereas a gemologist would start counting. I am neither so my authority is pretty suspect here.